Properties

Label 731.2.u.b.52.18
Level $731$
Weight $2$
Character 731.52
Analytic conductor $5.837$
Analytic rank $0$
Dimension $348$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [731,2,Mod(52,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.52");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.u (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(348\)
Relative dimension: \(29\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 52.18
Character \(\chi\) \(=\) 731.52
Dual form 731.2.u.b.239.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.429469 + 0.538537i) q^{2} +(-2.21655 - 0.334092i) q^{3} +(0.339463 - 1.48729i) q^{4} +(2.91429 + 1.98693i) q^{5} +(-0.772020 - 1.33718i) q^{6} +(1.74515 - 3.02268i) q^{7} +(2.18795 - 1.05366i) q^{8} +(1.93477 + 0.596798i) q^{9} +O(q^{10})\) \(q+(0.429469 + 0.538537i) q^{2} +(-2.21655 - 0.334092i) q^{3} +(0.339463 - 1.48729i) q^{4} +(2.91429 + 1.98693i) q^{5} +(-0.772020 - 1.33718i) q^{6} +(1.74515 - 3.02268i) q^{7} +(2.18795 - 1.05366i) q^{8} +(1.93477 + 0.596798i) q^{9} +(0.181562 + 2.42278i) q^{10} +(-0.929353 - 4.07176i) q^{11} +(-1.24933 + 3.18324i) q^{12} +(-0.113114 + 1.50940i) q^{13} +(2.37731 - 0.358322i) q^{14} +(-5.79586 - 5.37777i) q^{15} +(-1.24183 - 0.598032i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(0.509527 + 1.29825i) q^{18} +(-3.49066 + 1.07673i) q^{19} +(3.94443 - 3.65989i) q^{20} +(-4.87806 + 6.11690i) q^{21} +(1.79367 - 2.24919i) q^{22} +(0.911615 - 0.845855i) q^{23} +(-5.20172 + 1.60452i) q^{24} +(2.71849 + 6.92660i) q^{25} +(-0.861449 + 0.587326i) q^{26} +(1.96967 + 0.948542i) q^{27} +(-3.90318 - 3.62162i) q^{28} +(0.473046 - 0.0713001i) q^{29} +(0.406988 - 5.43087i) q^{30} +(1.59191 - 4.05613i) q^{31} +(-1.29202 - 5.66071i) q^{32} +(0.699619 + 9.33577i) q^{33} +(-0.658213 - 0.203032i) q^{34} +(11.0917 - 5.34149i) q^{35} +(1.54439 - 2.67497i) q^{36} +(-0.341336 - 0.591211i) q^{37} +(-2.07899 - 1.41743i) q^{38} +(0.755003 - 3.30788i) q^{39} +(8.46986 + 1.27663i) q^{40} +(-3.01062 - 3.77520i) q^{41} -5.38915 q^{42} +(1.97189 - 6.25393i) q^{43} -6.37135 q^{44} +(4.45269 + 5.58350i) q^{45} +(0.847035 + 0.127670i) q^{46} +(0.0684379 - 0.299846i) q^{47} +(2.55278 + 1.74045i) q^{48} +(-2.59107 - 4.48787i) q^{49} +(-2.56272 + 4.43877i) q^{50} +(2.01960 - 0.972589i) q^{51} +(2.20652 + 0.680620i) q^{52} +(-1.07902 - 14.3985i) q^{53} +(0.335086 + 1.46811i) q^{54} +(5.38190 - 13.7129i) q^{55} +(0.633410 - 8.45227i) q^{56} +(8.09697 - 1.22042i) q^{57} +(0.241556 + 0.224131i) q^{58} +(7.36714 + 3.54783i) q^{59} +(-9.96577 + 6.79455i) q^{60} +(4.08105 + 10.3983i) q^{61} +(2.86805 - 0.884677i) q^{62} +(5.18039 - 4.80670i) q^{63} +(0.774881 - 0.971669i) q^{64} +(-3.32872 + 4.17409i) q^{65} +(-4.72719 + 4.38619i) q^{66} +(15.3175 - 4.72483i) q^{67} +(0.557340 + 1.42008i) q^{68} +(-2.30324 + 1.57032i) q^{69} +(7.64014 + 3.67930i) q^{70} +(5.95771 + 5.52794i) q^{71} +(4.86201 - 0.732830i) q^{72} +(-1.04819 + 13.9871i) q^{73} +(0.171796 - 0.437729i) q^{74} +(-3.71156 - 16.2614i) q^{75} +(0.416449 + 5.55713i) q^{76} +(-13.9295 - 4.29668i) q^{77} +(2.10567 - 1.01404i) q^{78} +(-6.55442 + 11.3526i) q^{79} +(-2.43079 - 4.21026i) q^{80} +(-9.06769 - 6.18225i) q^{81} +(0.740116 - 3.24266i) q^{82} +(-16.4529 - 2.47987i) q^{83} +(7.44165 + 9.33154i) q^{84} -3.52718 q^{85} +(4.21484 - 1.62393i) q^{86} -1.07235 q^{87} +(-6.32363 - 7.92958i) q^{88} +(10.9024 + 1.64327i) q^{89} +(-1.09463 + 4.79588i) q^{90} +(4.36505 + 2.97604i) q^{91} +(-0.948569 - 1.64297i) q^{92} +(-4.88368 + 8.45878i) q^{93} +(0.190870 - 0.0919182i) q^{94} +(-12.3122 - 3.79781i) q^{95} +(0.972636 + 12.9789i) q^{96} +(1.18096 + 5.17411i) q^{97} +(1.30410 - 3.32279i) q^{98} +(0.631934 - 8.43257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{21}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.429469 + 0.538537i 0.303680 + 0.380803i 0.910133 0.414317i \(-0.135979\pi\)
−0.606452 + 0.795120i \(0.707408\pi\)
\(3\) −2.21655 0.334092i −1.27973 0.192888i −0.526232 0.850341i \(-0.676396\pi\)
−0.753495 + 0.657453i \(0.771634\pi\)
\(4\) 0.339463 1.48729i 0.169732 0.743643i
\(5\) 2.91429 + 1.98693i 1.30331 + 0.888582i 0.997971 0.0636624i \(-0.0202781\pi\)
0.305338 + 0.952244i \(0.401230\pi\)
\(6\) −0.772020 1.33718i −0.315176 0.545901i
\(7\) 1.74515 3.02268i 0.659603 1.14247i −0.321115 0.947040i \(-0.604058\pi\)
0.980718 0.195426i \(-0.0626090\pi\)
\(8\) 2.18795 1.05366i 0.773557 0.372525i
\(9\) 1.93477 + 0.596798i 0.644924 + 0.198933i
\(10\) 0.181562 + 2.42278i 0.0574150 + 0.766149i
\(11\) −0.929353 4.07176i −0.280210 1.22768i −0.897524 0.440965i \(-0.854636\pi\)
0.617314 0.786717i \(-0.288221\pi\)
\(12\) −1.24933 + 3.18324i −0.360650 + 0.918921i
\(13\) −0.113114 + 1.50940i −0.0313722 + 0.418633i 0.959302 + 0.282382i \(0.0911245\pi\)
−0.990674 + 0.136251i \(0.956495\pi\)
\(14\) 2.37731 0.358322i 0.635363 0.0957656i
\(15\) −5.79586 5.37777i −1.49648 1.38854i
\(16\) −1.24183 0.598032i −0.310457 0.149508i
\(17\) −0.826239 + 0.563320i −0.200392 + 0.136625i
\(18\) 0.509527 + 1.29825i 0.120097 + 0.306001i
\(19\) −3.49066 + 1.07673i −0.800813 + 0.247018i −0.668037 0.744128i \(-0.732865\pi\)
−0.132776 + 0.991146i \(0.542389\pi\)
\(20\) 3.94443 3.65989i 0.882000 0.818377i
\(21\) −4.87806 + 6.11690i −1.06448 + 1.33482i
\(22\) 1.79367 2.24919i 0.382411 0.479528i
\(23\) 0.911615 0.845855i 0.190085 0.176373i −0.579389 0.815051i \(-0.696709\pi\)
0.769474 + 0.638678i \(0.220518\pi\)
\(24\) −5.20172 + 1.60452i −1.06180 + 0.327521i
\(25\) 2.71849 + 6.92660i 0.543698 + 1.38532i
\(26\) −0.861449 + 0.587326i −0.168944 + 0.115184i
\(27\) 1.96967 + 0.948542i 0.379063 + 0.182547i
\(28\) −3.90318 3.62162i −0.737632 0.684422i
\(29\) 0.473046 0.0713001i 0.0878424 0.0132401i −0.104974 0.994475i \(-0.533476\pi\)
0.192816 + 0.981235i \(0.438238\pi\)
\(30\) 0.406988 5.43087i 0.0743054 0.991537i
\(31\) 1.59191 4.05613i 0.285916 0.728502i −0.713691 0.700461i \(-0.752978\pi\)
0.999607 0.0280412i \(-0.00892696\pi\)
\(32\) −1.29202 5.66071i −0.228399 1.00068i
\(33\) 0.699619 + 9.33577i 0.121788 + 1.62515i
\(34\) −0.658213 0.203032i −0.112883 0.0348197i
\(35\) 11.0917 5.34149i 1.87484 0.902876i
\(36\) 1.54439 2.67497i 0.257399 0.445828i
\(37\) −0.341336 0.591211i −0.0561153 0.0971945i 0.836603 0.547809i \(-0.184538\pi\)
−0.892718 + 0.450615i \(0.851205\pi\)
\(38\) −2.07899 1.41743i −0.337257 0.229938i
\(39\) 0.755003 3.30788i 0.120897 0.529685i
\(40\) 8.46986 + 1.27663i 1.33920 + 0.201852i
\(41\) −3.01062 3.77520i −0.470179 0.589586i 0.489036 0.872264i \(-0.337349\pi\)
−0.959215 + 0.282677i \(0.908777\pi\)
\(42\) −5.38915 −0.831564
\(43\) 1.97189 6.25393i 0.300710 0.953716i
\(44\) −6.37135 −0.960518
\(45\) 4.45269 + 5.58350i 0.663768 + 0.832339i
\(46\) 0.847035 + 0.127670i 0.124888 + 0.0188239i
\(47\) 0.0684379 0.299846i 0.00998270 0.0437370i −0.969691 0.244333i \(-0.921431\pi\)
0.979674 + 0.200596i \(0.0642880\pi\)
\(48\) 2.55278 + 1.74045i 0.368462 + 0.251213i
\(49\) −2.59107 4.48787i −0.370153 0.641124i
\(50\) −2.56272 + 4.43877i −0.362424 + 0.627737i
\(51\) 2.01960 0.972589i 0.282801 0.136190i
\(52\) 2.20652 + 0.680620i 0.305989 + 0.0943850i
\(53\) −1.07902 14.3985i −0.148215 1.97779i −0.202557 0.979271i \(-0.564925\pi\)
0.0543416 0.998522i \(-0.482694\pi\)
\(54\) 0.335086 + 1.46811i 0.0455994 + 0.199784i
\(55\) 5.38190 13.7129i 0.725695 1.84904i
\(56\) 0.633410 8.45227i 0.0846429 1.12948i
\(57\) 8.09697 1.22042i 1.07247 0.161649i
\(58\) 0.241556 + 0.224131i 0.0317179 + 0.0294299i
\(59\) 7.36714 + 3.54783i 0.959120 + 0.461888i 0.846875 0.531793i \(-0.178481\pi\)
0.112245 + 0.993681i \(0.464196\pi\)
\(60\) −9.96577 + 6.79455i −1.28658 + 0.877172i
\(61\) 4.08105 + 10.3983i 0.522525 + 1.33137i 0.911945 + 0.410312i \(0.134580\pi\)
−0.389420 + 0.921060i \(0.627325\pi\)
\(62\) 2.86805 0.884677i 0.364243 0.112354i
\(63\) 5.18039 4.80670i 0.652668 0.605587i
\(64\) 0.774881 0.971669i 0.0968601 0.121459i
\(65\) −3.32872 + 4.17409i −0.412877 + 0.517732i
\(66\) −4.72719 + 4.38619i −0.581877 + 0.539903i
\(67\) 15.3175 4.72483i 1.87133 0.577230i 0.875816 0.482645i \(-0.160324\pi\)
0.995517 0.0945849i \(-0.0301524\pi\)
\(68\) 0.557340 + 1.42008i 0.0675874 + 0.172210i
\(69\) −2.30324 + 1.57032i −0.277277 + 0.189044i
\(70\) 7.64014 + 3.67930i 0.913171 + 0.439760i
\(71\) 5.95771 + 5.52794i 0.707050 + 0.656046i 0.949374 0.314149i \(-0.101719\pi\)
−0.242324 + 0.970195i \(0.577910\pi\)
\(72\) 4.86201 0.732830i 0.572993 0.0863648i
\(73\) −1.04819 + 13.9871i −0.122682 + 1.63707i 0.508233 + 0.861220i \(0.330299\pi\)
−0.630915 + 0.775852i \(0.717320\pi\)
\(74\) 0.171796 0.437729i 0.0199709 0.0508849i
\(75\) −3.71156 16.2614i −0.428574 1.87771i
\(76\) 0.416449 + 5.55713i 0.0477700 + 0.637446i
\(77\) −13.9295 4.29668i −1.58741 0.489652i
\(78\) 2.10567 1.01404i 0.238420 0.114817i
\(79\) −6.55442 + 11.3526i −0.737430 + 1.27727i 0.216219 + 0.976345i \(0.430628\pi\)
−0.953649 + 0.300921i \(0.902706\pi\)
\(80\) −2.43079 4.21026i −0.271771 0.470721i
\(81\) −9.06769 6.18225i −1.00752 0.686916i
\(82\) 0.740116 3.24266i 0.0817321 0.358092i
\(83\) −16.4529 2.47987i −1.80594 0.272201i −0.842222 0.539131i \(-0.818753\pi\)
−0.963716 + 0.266929i \(0.913991\pi\)
\(84\) 7.44165 + 9.33154i 0.811951 + 1.01815i
\(85\) −3.52718 −0.382576
\(86\) 4.21484 1.62393i 0.454498 0.175113i
\(87\) −1.07235 −0.114968
\(88\) −6.32363 7.92958i −0.674101 0.845296i
\(89\) 10.9024 + 1.64327i 1.15565 + 0.174187i 0.698774 0.715343i \(-0.253729\pi\)
0.456878 + 0.889529i \(0.348967\pi\)
\(90\) −1.09463 + 4.79588i −0.115384 + 0.505530i
\(91\) 4.36505 + 2.97604i 0.457581 + 0.311974i
\(92\) −0.948569 1.64297i −0.0988951 0.171291i
\(93\) −4.88368 + 8.45878i −0.506414 + 0.877135i
\(94\) 0.190870 0.0919182i 0.0196868 0.00948064i
\(95\) −12.3122 3.79781i −1.26320 0.389647i
\(96\) 0.972636 + 12.9789i 0.0992693 + 1.32466i
\(97\) 1.18096 + 5.17411i 0.119908 + 0.525351i 0.998829 + 0.0483836i \(0.0154070\pi\)
−0.878921 + 0.476968i \(0.841736\pi\)
\(98\) 1.30410 3.32279i 0.131734 0.335652i
\(99\) 0.631934 8.43257i 0.0635117 0.847505i
\(100\) 11.2247 1.69185i 1.12247 0.169185i
\(101\) −5.79003 5.37236i −0.576129 0.534570i 0.337390 0.941365i \(-0.390456\pi\)
−0.913519 + 0.406795i \(0.866646\pi\)
\(102\) 1.39113 + 0.669934i 0.137743 + 0.0663333i
\(103\) −3.78772 + 2.58243i −0.373216 + 0.254454i −0.735373 0.677663i \(-0.762993\pi\)
0.362157 + 0.932117i \(0.382040\pi\)
\(104\) 1.34291 + 3.42168i 0.131683 + 0.335523i
\(105\) −26.3699 + 8.13404i −2.57344 + 0.793801i
\(106\) 7.29075 6.76482i 0.708140 0.657058i
\(107\) −6.13065 + 7.68759i −0.592672 + 0.743187i −0.984216 0.176972i \(-0.943370\pi\)
0.391544 + 0.920160i \(0.371941\pi\)
\(108\) 2.07938 2.60746i 0.200089 0.250903i
\(109\) 6.98813 6.48403i 0.669341 0.621058i −0.270480 0.962726i \(-0.587182\pi\)
0.939821 + 0.341668i \(0.110992\pi\)
\(110\) 9.69624 2.99089i 0.924500 0.285170i
\(111\) 0.559070 + 1.42449i 0.0530646 + 0.135206i
\(112\) −3.97483 + 2.70999i −0.375586 + 0.256070i
\(113\) −3.05240 1.46996i −0.287146 0.138282i 0.284767 0.958597i \(-0.408084\pi\)
−0.571912 + 0.820315i \(0.693798\pi\)
\(114\) 4.13464 + 3.83639i 0.387245 + 0.359310i
\(115\) 4.33736 0.653753i 0.404461 0.0609627i
\(116\) 0.0545379 0.727758i 0.00506372 0.0675706i
\(117\) −1.11966 + 2.85285i −0.103513 + 0.263746i
\(118\) 1.25332 + 5.49116i 0.115378 + 0.505502i
\(119\) 0.260830 + 3.48053i 0.0239102 + 0.319060i
\(120\) −18.3474 5.65942i −1.67488 0.516632i
\(121\) −5.80489 + 2.79549i −0.527717 + 0.254135i
\(122\) −3.84721 + 6.66356i −0.348310 + 0.603291i
\(123\) 5.41193 + 9.37374i 0.487978 + 0.845202i
\(124\) −5.49223 3.74454i −0.493216 0.336269i
\(125\) −1.91584 + 8.39386i −0.171358 + 0.750770i
\(126\) 4.81340 + 0.725504i 0.428812 + 0.0646330i
\(127\) 2.82978 + 3.54844i 0.251103 + 0.314873i 0.891367 0.453282i \(-0.149747\pi\)
−0.640265 + 0.768154i \(0.721175\pi\)
\(128\) −10.7565 −0.950750
\(129\) −6.46018 + 13.2034i −0.568787 + 1.16249i
\(130\) −3.67749 −0.322537
\(131\) 7.85366 + 9.84818i 0.686178 + 0.860440i 0.995907 0.0903850i \(-0.0288098\pi\)
−0.309729 + 0.950825i \(0.600238\pi\)
\(132\) 14.1224 + 2.12862i 1.22920 + 0.185272i
\(133\) −2.83712 + 12.4302i −0.246009 + 1.07784i
\(134\) 9.12290 + 6.21988i 0.788098 + 0.537316i
\(135\) 3.85550 + 6.67791i 0.331828 + 0.574743i
\(136\) −1.21422 + 2.10309i −0.104119 + 0.180339i
\(137\) 6.89453 3.32023i 0.589040 0.283666i −0.115527 0.993304i \(-0.536856\pi\)
0.704567 + 0.709638i \(0.251141\pi\)
\(138\) −1.83484 0.565975i −0.156192 0.0481790i
\(139\) −0.215725 2.87865i −0.0182976 0.244164i −0.998851 0.0479140i \(-0.984743\pi\)
0.980554 0.196250i \(-0.0628764\pi\)
\(140\) −4.17909 18.3098i −0.353198 1.54746i
\(141\) −0.251872 + 0.641760i −0.0212115 + 0.0540460i
\(142\) −0.418352 + 5.58253i −0.0351074 + 0.468475i
\(143\) 6.25105 0.942195i 0.522739 0.0787903i
\(144\) −2.04575 1.89818i −0.170479 0.158181i
\(145\) 1.52026 + 0.732119i 0.126251 + 0.0607991i
\(146\) −7.98276 + 5.44256i −0.660658 + 0.450429i
\(147\) 4.24389 + 10.8132i 0.350030 + 0.891862i
\(148\) −0.995171 + 0.306970i −0.0818025 + 0.0252327i
\(149\) 7.40542 6.87123i 0.606676 0.562913i −0.315869 0.948803i \(-0.602296\pi\)
0.922545 + 0.385890i \(0.126106\pi\)
\(150\) 7.16337 8.98258i 0.584887 0.733425i
\(151\) −9.50412 + 11.9178i −0.773434 + 0.969856i −0.999991 0.00414208i \(-0.998682\pi\)
0.226557 + 0.973998i \(0.427253\pi\)
\(152\) −6.50289 + 6.03380i −0.527454 + 0.489406i
\(153\) −1.93477 + 0.596798i −0.156417 + 0.0482483i
\(154\) −3.66837 9.34684i −0.295605 0.753190i
\(155\) 12.6985 8.65771i 1.01997 0.695404i
\(156\) −4.66347 2.24581i −0.373377 0.179809i
\(157\) 3.91254 + 3.63031i 0.312255 + 0.289730i 0.820694 0.571368i \(-0.193587\pi\)
−0.508439 + 0.861098i \(0.669777\pi\)
\(158\) −8.92871 + 1.34579i −0.710330 + 0.107065i
\(159\) −2.41873 + 32.2756i −0.191817 + 2.55963i
\(160\) 7.48211 19.0641i 0.591513 1.50715i
\(161\) −0.965850 4.23166i −0.0761196 0.333502i
\(162\) −0.564923 7.53837i −0.0443845 0.592270i
\(163\) −7.04558 2.17327i −0.551852 0.170224i 0.00627341 0.999980i \(-0.498003\pi\)
−0.558126 + 0.829756i \(0.688479\pi\)
\(164\) −6.63679 + 3.19611i −0.518246 + 0.249574i
\(165\) −16.5106 + 28.5972i −1.28535 + 2.22629i
\(166\) −5.73050 9.92551i −0.444773 0.770369i
\(167\) −11.2923 7.69898i −0.873826 0.595765i 0.0412037 0.999151i \(-0.486881\pi\)
−0.915030 + 0.403386i \(0.867833\pi\)
\(168\) −4.22782 + 18.5233i −0.326183 + 1.42910i
\(169\) 10.5893 + 1.59608i 0.814561 + 0.122775i
\(170\) −1.51481 1.89951i −0.116181 0.145686i
\(171\) −7.39623 −0.565604
\(172\) −8.63200 5.05574i −0.658184 0.385497i
\(173\) 4.18821 0.318424 0.159212 0.987244i \(-0.449105\pi\)
0.159212 + 0.987244i \(0.449105\pi\)
\(174\) −0.460542 0.577501i −0.0349136 0.0437802i
\(175\) 25.6811 + 3.87080i 1.94131 + 0.292605i
\(176\) −1.28095 + 5.61220i −0.0965551 + 0.423036i
\(177\) −15.1444 10.3252i −1.13832 0.776093i
\(178\) 3.79728 + 6.57708i 0.284618 + 0.492973i
\(179\) 2.05675 3.56240i 0.153729 0.266266i −0.778867 0.627190i \(-0.784205\pi\)
0.932596 + 0.360923i \(0.117538\pi\)
\(180\) 9.81578 4.72703i 0.731625 0.352332i
\(181\) 25.2618 + 7.79224i 1.87770 + 0.579193i 0.993753 + 0.111600i \(0.0355975\pi\)
0.883944 + 0.467593i \(0.154879\pi\)
\(182\) 0.271945 + 3.62885i 0.0201579 + 0.268989i
\(183\) −5.57186 24.4119i −0.411884 1.80458i
\(184\) 1.10332 2.81122i 0.0813381 0.207246i
\(185\) 0.179943 2.40117i 0.0132297 0.176538i
\(186\) −6.65275 + 1.00274i −0.487804 + 0.0735246i
\(187\) 3.06157 + 2.84072i 0.223884 + 0.207734i
\(188\) −0.422725 0.203573i −0.0308304 0.0148471i
\(189\) 6.30450 4.29833i 0.458585 0.312658i
\(190\) −3.24244 8.26161i −0.235232 0.599360i
\(191\) −17.4279 + 5.37581i −1.26104 + 0.388980i −0.852003 0.523537i \(-0.824612\pi\)
−0.409039 + 0.912517i \(0.634136\pi\)
\(192\) −2.04219 + 1.89488i −0.147382 + 0.136751i
\(193\) −8.64349 + 10.8386i −0.622172 + 0.780179i −0.988648 0.150248i \(-0.951993\pi\)
0.366476 + 0.930427i \(0.380564\pi\)
\(194\) −2.27927 + 2.85811i −0.163642 + 0.205200i
\(195\) 8.77282 8.13999i 0.628235 0.582917i
\(196\) −7.55431 + 2.33020i −0.539594 + 0.166443i
\(197\) 2.94641 + 7.50734i 0.209923 + 0.534876i 0.996591 0.0825008i \(-0.0262907\pi\)
−0.786668 + 0.617377i \(0.788195\pi\)
\(198\) 4.81265 3.28121i 0.342020 0.233185i
\(199\) 5.56532 + 2.68012i 0.394515 + 0.189988i 0.620615 0.784116i \(-0.286883\pi\)
−0.226100 + 0.974104i \(0.572597\pi\)
\(200\) 13.2462 + 12.2907i 0.936648 + 0.869083i
\(201\) −35.5306 + 5.35538i −2.50614 + 0.377739i
\(202\) 0.406578 5.42540i 0.0286067 0.381730i
\(203\) 0.610016 1.55430i 0.0428147 0.109090i
\(204\) −0.760938 3.33389i −0.0532763 0.233419i
\(205\) −1.27277 16.9839i −0.0888939 1.18621i
\(206\) −3.01744 0.930758i −0.210235 0.0648490i
\(207\) 2.26857 1.09249i 0.157677 0.0759331i
\(208\) 1.04314 1.80677i 0.0723287 0.125277i
\(209\) 7.62824 + 13.2125i 0.527656 + 0.913927i
\(210\) −15.7055 10.7079i −1.08379 0.738913i
\(211\) 1.98494 8.69660i 0.136649 0.598699i −0.859509 0.511121i \(-0.829230\pi\)
0.996158 0.0875774i \(-0.0279125\pi\)
\(212\) −21.7810 3.28296i −1.49593 0.225475i
\(213\) −11.3587 14.2434i −0.778288 0.975942i
\(214\) −6.77298 −0.462991
\(215\) 18.1728 14.3078i 1.23937 0.975781i
\(216\) 5.30897 0.361230
\(217\) −9.48226 11.8904i −0.643698 0.807172i
\(218\) 6.49308 + 0.978674i 0.439767 + 0.0662841i
\(219\) 6.99636 30.6531i 0.472770 2.07134i
\(220\) −18.5680 12.6594i −1.25185 0.853499i
\(221\) −0.756818 1.31085i −0.0509091 0.0881771i
\(222\) −0.527036 + 0.912854i −0.0353724 + 0.0612667i
\(223\) 1.11999 0.539360i 0.0750002 0.0361182i −0.396008 0.918247i \(-0.629605\pi\)
0.471008 + 0.882129i \(0.343890\pi\)
\(224\) −19.3653 5.97340i −1.29390 0.399115i
\(225\) 1.12588 + 15.0238i 0.0750585 + 1.00159i
\(226\) −0.519284 2.27513i −0.0345423 0.151339i
\(227\) −3.72267 + 9.48522i −0.247083 + 0.629556i −0.999578 0.0290412i \(-0.990755\pi\)
0.752496 + 0.658597i \(0.228850\pi\)
\(228\) 0.933508 12.4568i 0.0618231 0.824972i
\(229\) −7.78067 + 1.17275i −0.514161 + 0.0774974i −0.400998 0.916079i \(-0.631336\pi\)
−0.113164 + 0.993576i \(0.536098\pi\)
\(230\) 2.21483 + 2.05507i 0.146042 + 0.135507i
\(231\) 29.4400 + 14.1776i 1.93701 + 0.932814i
\(232\) 0.959873 0.654431i 0.0630188 0.0429655i
\(233\) 4.94958 + 12.6113i 0.324258 + 0.826195i 0.996321 + 0.0857011i \(0.0273130\pi\)
−0.672063 + 0.740494i \(0.734592\pi\)
\(234\) −2.01722 + 0.622231i −0.131870 + 0.0406765i
\(235\) 0.795221 0.737857i 0.0518745 0.0481325i
\(236\) 7.77751 9.75268i 0.506273 0.634846i
\(237\) 18.3210 22.9738i 1.19008 1.49231i
\(238\) −1.76238 + 1.63525i −0.114238 + 0.105997i
\(239\) −2.17039 + 0.669475i −0.140391 + 0.0433048i −0.364154 0.931339i \(-0.618642\pi\)
0.223764 + 0.974643i \(0.428166\pi\)
\(240\) 3.98137 + 10.1444i 0.256996 + 0.654816i
\(241\) 2.44331 1.66582i 0.157387 0.107305i −0.482066 0.876135i \(-0.660113\pi\)
0.639453 + 0.768830i \(0.279161\pi\)
\(242\) −3.99849 1.92557i −0.257033 0.123781i
\(243\) 13.2259 + 12.2718i 0.848440 + 0.787237i
\(244\) 16.8507 2.53983i 1.07875 0.162596i
\(245\) 1.36594 18.2272i 0.0872668 1.16449i
\(246\) −2.72385 + 6.94026i −0.173666 + 0.442495i
\(247\) −1.23037 5.39061i −0.0782867 0.342997i
\(248\) −0.790758 10.5519i −0.0502132 0.670049i
\(249\) 35.6402 + 10.9935i 2.25860 + 0.696687i
\(250\) −5.34320 + 2.57315i −0.337934 + 0.162740i
\(251\) −13.1492 + 22.7750i −0.829968 + 1.43755i 0.0680952 + 0.997679i \(0.478308\pi\)
−0.898063 + 0.439867i \(0.855025\pi\)
\(252\) −5.39039 9.33642i −0.339562 0.588139i
\(253\) −4.29133 2.92578i −0.269794 0.183942i
\(254\) −0.695660 + 3.04789i −0.0436496 + 0.191241i
\(255\) 7.81817 + 1.17840i 0.489593 + 0.0737943i
\(256\) −6.16935 7.73612i −0.385584 0.483507i
\(257\) 2.30137 0.143556 0.0717778 0.997421i \(-0.477133\pi\)
0.0717778 + 0.997421i \(0.477133\pi\)
\(258\) −9.88496 + 2.19139i −0.615411 + 0.136430i
\(259\) −2.38272 −0.148055
\(260\) 5.07808 + 6.36771i 0.314929 + 0.394909i
\(261\) 0.957787 + 0.144363i 0.0592856 + 0.00893586i
\(262\) −1.93071 + 8.45898i −0.119279 + 0.522597i
\(263\) 8.14812 + 5.55529i 0.502434 + 0.342554i 0.787868 0.615845i \(-0.211185\pi\)
−0.285433 + 0.958399i \(0.592137\pi\)
\(264\) 11.3675 + 19.6890i 0.699619 + 1.21178i
\(265\) 25.4643 44.1055i 1.56426 2.70938i
\(266\) −7.91259 + 3.81050i −0.485152 + 0.233637i
\(267\) −23.6167 7.28480i −1.44532 0.445823i
\(268\) −1.82744 24.3854i −0.111628 1.48958i
\(269\) 4.11643 + 18.0352i 0.250983 + 1.09963i 0.930593 + 0.366055i \(0.119292\pi\)
−0.679610 + 0.733573i \(0.737851\pi\)
\(270\) −1.94049 + 4.94428i −0.118094 + 0.300900i
\(271\) −0.156577 + 2.08937i −0.00951136 + 0.126920i −0.999938 0.0111185i \(-0.996461\pi\)
0.990427 + 0.138039i \(0.0440798\pi\)
\(272\) 1.36293 0.205428i 0.0826397 0.0124559i
\(273\) −8.68109 8.05487i −0.525403 0.487503i
\(274\) 4.74905 + 2.28702i 0.286901 + 0.138164i
\(275\) 25.6770 17.5063i 1.54838 1.05567i
\(276\) 1.55365 + 3.95864i 0.0935188 + 0.238282i
\(277\) −30.5445 + 9.42174i −1.83524 + 0.566098i −0.835378 + 0.549676i \(0.814751\pi\)
−0.999865 + 0.0164220i \(0.994772\pi\)
\(278\) 1.45761 1.35247i 0.0874218 0.0811156i
\(279\) 5.50068 6.89763i 0.329317 0.412951i
\(280\) 18.6400 23.3738i 1.11395 1.39685i
\(281\) −3.21689 + 2.98484i −0.191904 + 0.178061i −0.770273 0.637715i \(-0.779880\pi\)
0.578369 + 0.815775i \(0.303689\pi\)
\(282\) −0.453783 + 0.139974i −0.0270224 + 0.00833530i
\(283\) −10.9694 27.9496i −0.652065 1.66143i −0.746074 0.665863i \(-0.768064\pi\)
0.0940097 0.995571i \(-0.470032\pi\)
\(284\) 10.2441 6.98428i 0.607873 0.414441i
\(285\) 26.0218 + 12.5314i 1.54140 + 0.742298i
\(286\) 3.19204 + 2.96178i 0.188749 + 0.175134i
\(287\) −16.6652 + 2.51187i −0.983715 + 0.148271i
\(288\) 0.878538 11.7233i 0.0517683 0.690800i
\(289\) 0.365341 0.930874i 0.0214906 0.0547573i
\(290\) 0.258631 + 1.13314i 0.0151874 + 0.0665402i
\(291\) −0.889027 11.8632i −0.0521157 0.695435i
\(292\) 20.4471 + 6.30708i 1.19657 + 0.369094i
\(293\) −1.33254 + 0.641716i −0.0778477 + 0.0374895i −0.472402 0.881383i \(-0.656613\pi\)
0.394555 + 0.918872i \(0.370899\pi\)
\(294\) −4.00072 + 6.92945i −0.233327 + 0.404134i
\(295\) 14.4207 + 24.9774i 0.839605 + 1.45424i
\(296\) −1.36976 0.933888i −0.0796158 0.0542811i
\(297\) 2.03172 8.90155i 0.117892 0.516520i
\(298\) 6.88081 + 1.03712i 0.398595 + 0.0600785i
\(299\) 1.17362 + 1.47167i 0.0678722 + 0.0851091i
\(300\) −25.4453 −1.46909
\(301\) −15.4624 16.8744i −0.891238 0.972625i
\(302\) −10.4999 −0.604201
\(303\) 11.0390 + 13.8425i 0.634176 + 0.795232i
\(304\) 4.97872 + 0.750421i 0.285549 + 0.0430396i
\(305\) −8.76741 + 38.4125i −0.502021 + 2.19950i
\(306\) −1.15232 0.785640i −0.0658739 0.0449121i
\(307\) 0.610553 + 1.05751i 0.0348461 + 0.0603552i 0.882923 0.469519i \(-0.155573\pi\)
−0.848076 + 0.529874i \(0.822239\pi\)
\(308\) −11.1189 + 19.2586i −0.633561 + 1.09736i
\(309\) 9.25846 4.45864i 0.526695 0.253643i
\(310\) 10.1161 + 3.12041i 0.574557 + 0.177227i
\(311\) 0.465992 + 6.21823i 0.0264240 + 0.352604i 0.994707 + 0.102749i \(0.0327638\pi\)
−0.968283 + 0.249855i \(0.919617\pi\)
\(312\) −1.83348 8.03299i −0.103800 0.454779i
\(313\) −8.57538 + 21.8497i −0.484709 + 1.23502i 0.454215 + 0.890892i \(0.349920\pi\)
−0.938924 + 0.344126i \(0.888175\pi\)
\(314\) −0.274740 + 3.66616i −0.0155045 + 0.206893i
\(315\) 24.6477 3.71505i 1.38874 0.209319i
\(316\) 14.6596 + 13.6021i 0.824665 + 0.765177i
\(317\) 15.0780 + 7.26119i 0.846866 + 0.407829i 0.806413 0.591352i \(-0.201406\pi\)
0.0404528 + 0.999181i \(0.487120\pi\)
\(318\) −18.4204 + 12.5588i −1.03296 + 0.704263i
\(319\) −0.729944 1.85987i −0.0408690 0.104132i
\(320\) 4.18886 1.29209i 0.234165 0.0722302i
\(321\) 16.1573 14.9918i 0.901811 0.836758i
\(322\) 1.86411 2.33751i 0.103883 0.130265i
\(323\) 2.27758 2.85600i 0.126728 0.158912i
\(324\) −12.2729 + 11.3876i −0.681829 + 0.632645i
\(325\) −10.7625 + 3.31980i −0.596998 + 0.184150i
\(326\) −1.85547 4.72766i −0.102765 0.261841i
\(327\) −17.6558 + 12.0375i −0.976369 + 0.665677i
\(328\) −10.5649 5.08776i −0.583346 0.280925i
\(329\) −0.786905 0.730141i −0.0433835 0.0402540i
\(330\) −22.4915 + 3.39004i −1.23811 + 0.186616i
\(331\) 0.381324 5.08841i 0.0209594 0.279684i −0.976870 0.213834i \(-0.931405\pi\)
0.997829 0.0658506i \(-0.0209761\pi\)
\(332\) −9.27343 + 23.6283i −0.508946 + 1.29677i
\(333\) −0.307574 1.34757i −0.0168549 0.0738463i
\(334\) −0.703519 9.38781i −0.0384948 0.513678i
\(335\) 54.0276 + 16.6653i 2.95184 + 0.910523i
\(336\) 9.71580 4.67889i 0.530041 0.255254i
\(337\) −6.86005 + 11.8820i −0.373691 + 0.647251i −0.990130 0.140151i \(-0.955241\pi\)
0.616439 + 0.787402i \(0.288575\pi\)
\(338\) 3.68823 + 6.38820i 0.200613 + 0.347472i
\(339\) 6.27470 + 4.27802i 0.340795 + 0.232350i
\(340\) −1.19735 + 5.24592i −0.0649352 + 0.284500i
\(341\) −17.9950 2.71232i −0.974486 0.146880i
\(342\) −3.17645 3.98314i −0.171763 0.215384i
\(343\) 6.34486 0.342590
\(344\) −2.27513 15.7610i −0.122667 0.849775i
\(345\) −9.83241 −0.529359
\(346\) 1.79871 + 2.25551i 0.0966990 + 0.121257i
\(347\) 35.4290 + 5.34006i 1.90193 + 0.286669i 0.991814 0.127691i \(-0.0407566\pi\)
0.910113 + 0.414360i \(0.135995\pi\)
\(348\) −0.364024 + 1.59489i −0.0195137 + 0.0854953i
\(349\) 15.4074 + 10.5046i 0.824740 + 0.562298i 0.900514 0.434827i \(-0.143190\pi\)
−0.0757741 + 0.997125i \(0.524143\pi\)
\(350\) 8.94466 + 15.4926i 0.478112 + 0.828114i
\(351\) −1.65453 + 2.86573i −0.0883122 + 0.152961i
\(352\) −21.8483 + 10.5216i −1.16452 + 0.560803i
\(353\) −19.3682 5.97431i −1.03087 0.317981i −0.267235 0.963631i \(-0.586110\pi\)
−0.763633 + 0.645651i \(0.776586\pi\)
\(354\) −0.943503 12.5902i −0.0501466 0.669160i
\(355\) 6.37885 + 27.9476i 0.338554 + 1.48330i
\(356\) 6.14498 15.6572i 0.325683 0.829828i
\(357\) 0.584674 7.80193i 0.0309442 0.412922i
\(358\) 2.80180 0.422303i 0.148080 0.0223194i
\(359\) 26.8771 + 24.9383i 1.41852 + 1.31619i 0.881142 + 0.472852i \(0.156775\pi\)
0.537378 + 0.843342i \(0.319415\pi\)
\(360\) 15.6254 + 7.52478i 0.823529 + 0.396591i
\(361\) −4.67314 + 3.18609i −0.245955 + 0.167689i
\(362\) 6.65276 + 16.9510i 0.349661 + 0.890923i
\(363\) 13.8008 4.25698i 0.724354 0.223434i
\(364\) 5.90799 5.48182i 0.309663 0.287325i
\(365\) −30.8462 + 38.6799i −1.61456 + 2.02460i
\(366\) 10.7538 13.4848i 0.562110 0.704863i
\(367\) −15.5424 + 14.4213i −0.811308 + 0.752784i −0.972191 0.234190i \(-0.924756\pi\)
0.160883 + 0.986973i \(0.448566\pi\)
\(368\) −1.63792 + 0.505230i −0.0853823 + 0.0263369i
\(369\) −3.57183 9.10088i −0.185942 0.473773i
\(370\) 1.37040 0.934322i 0.0712437 0.0485731i
\(371\) −45.4053 21.8660i −2.35733 1.13523i
\(372\) 10.9228 + 10.1349i 0.566320 + 0.525469i
\(373\) 6.13277 0.924366i 0.317543 0.0478619i 0.0116629 0.999932i \(-0.496288\pi\)
0.305880 + 0.952070i \(0.401049\pi\)
\(374\) −0.214985 + 2.86877i −0.0111166 + 0.148341i
\(375\) 7.05089 17.9654i 0.364106 0.927728i
\(376\) −0.166197 0.728158i −0.00857097 0.0375519i
\(377\) 0.0541125 + 0.722082i 0.00278694 + 0.0371891i
\(378\) 5.02240 + 1.54920i 0.258324 + 0.0796825i
\(379\) 22.5594 10.8640i 1.15880 0.558048i 0.247134 0.968981i \(-0.420511\pi\)
0.911666 + 0.410933i \(0.134797\pi\)
\(380\) −9.82796 + 17.0225i −0.504164 + 0.873237i
\(381\) −5.08686 8.81070i −0.260608 0.451386i
\(382\) −10.3798 7.07685i −0.531078 0.362083i
\(383\) 5.40345 23.6741i 0.276104 1.20969i −0.626571 0.779365i \(-0.715542\pi\)
0.902674 0.430324i \(-0.141601\pi\)
\(384\) 23.8424 + 3.59366i 1.21670 + 0.183388i
\(385\) −32.0574 40.1987i −1.63380 2.04872i
\(386\) −9.54910 −0.486036
\(387\) 7.54749 10.9231i 0.383661 0.555253i
\(388\) 8.09627 0.411026
\(389\) 15.4678 + 19.3960i 0.784249 + 0.983418i 0.999976 + 0.00696372i \(0.00221664\pi\)
−0.215726 + 0.976454i \(0.569212\pi\)
\(390\) 8.15134 + 1.22862i 0.412759 + 0.0622134i
\(391\) −0.276725 + 1.21241i −0.0139946 + 0.0613142i
\(392\) −10.3978 7.08911i −0.525169 0.358054i
\(393\) −14.1179 24.4529i −0.712152 1.23348i
\(394\) −2.77759 + 4.81092i −0.139933 + 0.242371i
\(395\) −41.6583 + 20.0616i −2.09606 + 1.00941i
\(396\) −12.3271 3.80241i −0.619461 0.191078i
\(397\) −0.949661 12.6723i −0.0476621 0.636007i −0.968971 0.247175i \(-0.920498\pi\)
0.921309 0.388832i \(-0.127121\pi\)
\(398\) 0.946790 + 4.14816i 0.0474583 + 0.207928i
\(399\) 10.4414 26.6044i 0.522726 1.33188i
\(400\) 0.766436 10.2274i 0.0383218 0.511369i
\(401\) −30.0002 + 4.52180i −1.49814 + 0.225808i −0.846364 0.532606i \(-0.821213\pi\)
−0.651774 + 0.758413i \(0.725975\pi\)
\(402\) −18.1434 16.8346i −0.904909 0.839633i
\(403\) 5.94227 + 2.86164i 0.296005 + 0.142549i
\(404\) −9.95573 + 6.78770i −0.495316 + 0.337701i
\(405\) −14.1422 36.0337i −0.702731 1.79053i
\(406\) 1.09903 0.339005i 0.0545439 0.0168246i
\(407\) −2.09005 + 1.93928i −0.103600 + 0.0961267i
\(408\) 3.39401 4.25595i 0.168028 0.210701i
\(409\) −0.980648 + 1.22969i −0.0484899 + 0.0608044i −0.805485 0.592616i \(-0.798095\pi\)
0.756995 + 0.653420i \(0.226667\pi\)
\(410\) 8.59984 7.97949i 0.424716 0.394079i
\(411\) −16.3914 + 5.05606i −0.808526 + 0.249397i
\(412\) 2.55501 + 6.51007i 0.125876 + 0.320728i
\(413\) 23.5807 16.0770i 1.16033 0.791099i
\(414\) 1.56263 + 0.752521i 0.0767989 + 0.0369844i
\(415\) −43.0211 39.9178i −2.11182 1.95949i
\(416\) 8.69045 1.30987i 0.426084 0.0642219i
\(417\) −0.483567 + 6.45275i −0.0236804 + 0.315993i
\(418\) −3.83933 + 9.78245i −0.187788 + 0.478475i
\(419\) −8.61604 37.7494i −0.420921 1.84418i −0.527064 0.849826i \(-0.676707\pi\)
0.106142 0.994351i \(-0.466150\pi\)
\(420\) 3.14603 + 41.9808i 0.153510 + 2.04845i
\(421\) −4.86129 1.49951i −0.236925 0.0730817i 0.174019 0.984742i \(-0.444325\pi\)
−0.410944 + 0.911661i \(0.634801\pi\)
\(422\) 5.53591 2.66595i 0.269484 0.129777i
\(423\) 0.311359 0.539290i 0.0151388 0.0262212i
\(424\) −17.5320 30.3664i −0.851431 1.47472i
\(425\) −6.14802 4.19165i −0.298223 0.203325i
\(426\) 2.79238 12.2342i 0.135291 0.592749i
\(427\) 38.5529 + 5.81092i 1.86571 + 0.281210i
\(428\) 9.35251 + 11.7277i 0.452071 + 0.566879i
\(429\) −14.1706 −0.684162
\(430\) 15.5099 + 3.64197i 0.747954 + 0.175631i
\(431\) 1.45345 0.0700102 0.0350051 0.999387i \(-0.488855\pi\)
0.0350051 + 0.999387i \(0.488855\pi\)
\(432\) −1.87873 2.35585i −0.0903902 0.113346i
\(433\) 21.8184 + 3.28859i 1.04853 + 0.158040i 0.650633 0.759392i \(-0.274504\pi\)
0.397892 + 0.917432i \(0.369742\pi\)
\(434\) 2.33107 10.2131i 0.111895 0.490245i
\(435\) −3.12514 2.13069i −0.149839 0.102159i
\(436\) −7.27140 12.5944i −0.348237 0.603164i
\(437\) −2.27139 + 3.93416i −0.108655 + 0.188196i
\(438\) 19.5125 9.39674i 0.932345 0.448994i
\(439\) 36.3964 + 11.2268i 1.73710 + 0.535825i 0.991448 0.130506i \(-0.0416601\pi\)
0.745656 + 0.666331i \(0.232136\pi\)
\(440\) −2.67337 35.6737i −0.127448 1.70068i
\(441\) −2.33478 10.2293i −0.111180 0.487112i
\(442\) 0.380910 0.970543i 0.0181180 0.0461640i
\(443\) 1.08250 14.4449i 0.0514310 0.686298i −0.910588 0.413315i \(-0.864371\pi\)
0.962019 0.272983i \(-0.0880103\pi\)
\(444\) 2.30841 0.347936i 0.109552 0.0165123i
\(445\) 28.5077 + 26.4513i 1.35139 + 1.25391i
\(446\) 0.771467 + 0.371519i 0.0365300 + 0.0175919i
\(447\) −18.7101 + 12.7564i −0.884959 + 0.603355i
\(448\) −1.58477 4.03792i −0.0748732 0.190774i
\(449\) 3.54215 1.09261i 0.167164 0.0515634i −0.210043 0.977692i \(-0.567360\pi\)
0.377208 + 0.926129i \(0.376884\pi\)
\(450\) −7.60734 + 7.05858i −0.358613 + 0.332745i
\(451\) −12.5738 + 15.7670i −0.592076 + 0.742439i
\(452\) −3.22243 + 4.04079i −0.151570 + 0.190063i
\(453\) 25.0480 23.2412i 1.17686 1.09197i
\(454\) −6.70691 + 2.06881i −0.314771 + 0.0970940i
\(455\) 6.80783 + 17.3461i 0.319156 + 0.813196i
\(456\) 16.4298 11.2017i 0.769398 0.524567i
\(457\) 2.17524 + 1.04754i 0.101754 + 0.0490019i 0.484068 0.875030i \(-0.339159\pi\)
−0.382315 + 0.924032i \(0.624873\pi\)
\(458\) −3.97313 3.68652i −0.185652 0.172260i
\(459\) −2.16175 + 0.325831i −0.100902 + 0.0152085i
\(460\) 0.500059 6.67283i 0.0233154 0.311122i
\(461\) −9.76976 + 24.8929i −0.455023 + 1.15938i 0.500833 + 0.865544i \(0.333027\pi\)
−0.955856 + 0.293836i \(0.905068\pi\)
\(462\) 5.00842 + 21.9433i 0.233013 + 1.02090i
\(463\) −1.42123 18.9651i −0.0660504 0.881381i −0.927568 0.373654i \(-0.878105\pi\)
0.861518 0.507727i \(-0.169514\pi\)
\(464\) −0.630080 0.194354i −0.0292507 0.00902266i
\(465\) −31.0394 + 14.9478i −1.43942 + 0.693188i
\(466\) −4.66597 + 8.08170i −0.216147 + 0.374377i
\(467\) −19.3067 33.4402i −0.893408 1.54743i −0.835763 0.549090i \(-0.814974\pi\)
−0.0576447 0.998337i \(-0.518359\pi\)
\(468\) 3.86291 + 2.63369i 0.178563 + 0.121742i
\(469\) 12.4497 54.5455i 0.574872 2.51868i
\(470\) 0.738886 + 0.111369i 0.0340823 + 0.00513708i
\(471\) −7.45950 9.35392i −0.343716 0.431006i
\(472\) 19.8571 0.913998
\(473\) −27.2971 2.21695i −1.25512 0.101936i
\(474\) 20.2406 0.929681
\(475\) −16.9474 21.2514i −0.777600 0.975080i
\(476\) 5.26509 + 0.793585i 0.241325 + 0.0363739i
\(477\) 6.50537 28.5019i 0.297860 1.30501i
\(478\) −1.29265 0.881314i −0.0591245 0.0403104i
\(479\) −3.18238 5.51205i −0.145407 0.251852i 0.784118 0.620612i \(-0.213116\pi\)
−0.929525 + 0.368760i \(0.879782\pi\)
\(480\) −22.9537 + 39.7569i −1.04769 + 1.81465i
\(481\) 0.930986 0.448339i 0.0424493 0.0204425i
\(482\) 1.94643 + 0.600394i 0.0886575 + 0.0273472i
\(483\) 0.727094 + 9.70239i 0.0330839 + 0.441474i
\(484\) 2.18714 + 9.58249i 0.0994155 + 0.435568i
\(485\) −6.83894 + 17.4253i −0.310540 + 0.791244i
\(486\) −0.928726 + 12.3930i −0.0421278 + 0.562157i
\(487\) −3.24642 + 0.489319i −0.147109 + 0.0221731i −0.222184 0.975005i \(-0.571319\pi\)
0.0750748 + 0.997178i \(0.476080\pi\)
\(488\) 19.8855 + 18.4510i 0.900172 + 0.835238i
\(489\) 14.8908 + 7.17104i 0.673386 + 0.324286i
\(490\) 10.4027 7.09241i 0.469944 0.320403i
\(491\) −3.23247 8.23620i −0.145879 0.371694i 0.839193 0.543833i \(-0.183028\pi\)
−0.985073 + 0.172139i \(0.944932\pi\)
\(492\) 15.7786 4.86705i 0.711354 0.219424i
\(493\) −0.350684 + 0.325387i −0.0157940 + 0.0146547i
\(494\) 2.37464 2.97770i 0.106840 0.133973i
\(495\) 18.5966 23.3193i 0.835853 1.04813i
\(496\) −4.40257 + 4.08499i −0.197681 + 0.183422i
\(497\) 27.1063 8.36118i 1.21588 0.375050i
\(498\) 9.38592 + 23.9149i 0.420593 + 1.07165i
\(499\) 22.9018 15.6142i 1.02523 0.698988i 0.0708178 0.997489i \(-0.477439\pi\)
0.954409 + 0.298501i \(0.0964867\pi\)
\(500\) 11.8337 + 5.69881i 0.529220 + 0.254859i
\(501\) 22.4579 + 20.8379i 1.00334 + 0.930967i
\(502\) −17.9123 + 2.69985i −0.799467 + 0.120500i
\(503\) −1.67066 + 22.2934i −0.0744912 + 0.994016i 0.827277 + 0.561795i \(0.189889\pi\)
−0.901768 + 0.432221i \(0.857730\pi\)
\(504\) 6.26980 15.9752i 0.279279 0.711592i
\(505\) −6.19932 27.1610i −0.275866 1.20865i
\(506\) −0.267353 3.56757i −0.0118853 0.158598i
\(507\) −22.9385 7.07559i −1.01873 0.314238i
\(508\) 6.23815 3.00413i 0.276773 0.133287i
\(509\) 11.5998 20.0915i 0.514154 0.890540i −0.485711 0.874119i \(-0.661439\pi\)
0.999865 0.0164211i \(-0.00522723\pi\)
\(510\) 2.72305 + 4.71646i 0.120579 + 0.208848i
\(511\) 40.4494 + 27.5780i 1.78938 + 1.21998i
\(512\) −3.27046 + 14.3288i −0.144535 + 0.633249i
\(513\) −7.89677 1.19025i −0.348651 0.0525507i
\(514\) 0.988367 + 1.23937i 0.0435950 + 0.0546664i
\(515\) −16.1696 −0.712519
\(516\) 17.4442 + 14.0902i 0.767938 + 0.620287i
\(517\) −1.28450 −0.0564925
\(518\) −1.02331 1.28319i −0.0449615 0.0563799i
\(519\) −9.28339 1.39925i −0.407496 0.0614201i
\(520\) −2.88501 + 12.6400i −0.126516 + 0.554302i
\(521\) −7.39090 5.03903i −0.323801 0.220764i 0.390499 0.920603i \(-0.372303\pi\)
−0.714300 + 0.699839i \(0.753255\pi\)
\(522\) 0.333595 + 0.577804i 0.0146011 + 0.0252898i
\(523\) −8.07881 + 13.9929i −0.353261 + 0.611867i −0.986819 0.161829i \(-0.948261\pi\)
0.633557 + 0.773696i \(0.281594\pi\)
\(524\) 17.3131 8.33755i 0.756326 0.364227i
\(525\) −55.6303 17.1597i −2.42790 0.748909i
\(526\) 0.507633 + 6.77389i 0.0221338 + 0.295356i
\(527\) 0.969598 + 4.24809i 0.0422364 + 0.185050i
\(528\) 4.71428 12.0118i 0.205163 0.522746i
\(529\) −1.60322 + 21.3935i −0.0697053 + 0.930152i
\(530\) 34.6886 5.22846i 1.50678 0.227110i
\(531\) 12.1364 + 11.2609i 0.526675 + 0.488683i
\(532\) 17.5242 + 8.43920i 0.759770 + 0.365886i
\(533\) 6.03884 4.11721i 0.261571 0.178336i
\(534\) −6.21952 15.8471i −0.269145 0.685771i
\(535\) −33.1412 + 10.2227i −1.43282 + 0.441966i
\(536\) 28.5356 26.4772i 1.23255 1.14364i
\(537\) −5.74907 + 7.20911i −0.248091 + 0.311096i
\(538\) −7.94477 + 9.96243i −0.342523 + 0.429511i
\(539\) −15.8655 + 14.7210i −0.683376 + 0.634080i
\(540\) 11.2408 3.46732i 0.483726 0.149210i
\(541\) 14.5841 + 37.1597i 0.627019 + 1.59762i 0.791452 + 0.611231i \(0.209325\pi\)
−0.164433 + 0.986388i \(0.552579\pi\)
\(542\) −1.19245 + 0.812997i −0.0512200 + 0.0349212i
\(543\) −53.3909 25.7117i −2.29122 1.10339i
\(544\) 4.25631 + 3.94928i 0.182488 + 0.169324i
\(545\) 33.2487 5.01144i 1.42422 0.214667i
\(546\) 0.609589 8.13440i 0.0260880 0.348120i
\(547\) 9.97378 25.4128i 0.426448 1.08657i −0.542664 0.839950i \(-0.682584\pi\)
0.969112 0.246622i \(-0.0793205\pi\)
\(548\) −2.59769 11.3812i −0.110968 0.486182i
\(549\) 1.69019 + 22.5540i 0.0721355 + 0.962581i
\(550\) 20.4553 + 6.30962i 0.872216 + 0.269043i
\(551\) −1.57447 + 0.758226i −0.0670748 + 0.0323015i
\(552\) −3.38478 + 5.86261i −0.144066 + 0.249529i
\(553\) 22.8768 + 39.6239i 0.972823 + 1.68498i
\(554\) −18.1919 12.4030i −0.772899 0.526954i
\(555\) −1.20106 + 5.26220i −0.0509823 + 0.223368i
\(556\) −4.35461 0.656351i −0.184676 0.0278355i
\(557\) −1.50498 1.88719i −0.0637681 0.0799627i 0.748924 0.662655i \(-0.230571\pi\)
−0.812693 + 0.582693i \(0.801999\pi\)
\(558\) 6.07700 0.257260
\(559\) 9.21666 + 3.68378i 0.389823 + 0.155807i
\(560\) −16.9684 −0.717044
\(561\) −5.83708 7.31946i −0.246442 0.309028i
\(562\) −2.98900 0.450520i −0.126084 0.0190040i
\(563\) 7.75200 33.9637i 0.326708 1.43140i −0.498656 0.866800i \(-0.666173\pi\)
0.825364 0.564601i \(-0.190970\pi\)
\(564\) 0.868980 + 0.592460i 0.0365906 + 0.0249471i
\(565\) −5.97487 10.3488i −0.251365 0.435377i
\(566\) 10.3409 17.9109i 0.434660 0.752853i
\(567\) −34.5114 + 16.6198i −1.44934 + 0.697967i
\(568\) 18.8597 + 5.81746i 0.791337 + 0.244095i
\(569\) −2.28751 30.5247i −0.0958974 1.27966i −0.812822 0.582512i \(-0.802070\pi\)
0.716925 0.697150i \(-0.245549\pi\)
\(570\) 4.42691 + 19.3956i 0.185423 + 0.812391i
\(571\) −13.5951 + 34.6398i −0.568939 + 1.44963i 0.299626 + 0.954057i \(0.403138\pi\)
−0.868565 + 0.495576i \(0.834957\pi\)
\(572\) 0.720690 9.61694i 0.0301336 0.402105i
\(573\) 40.4260 6.09323i 1.68882 0.254549i
\(574\) −8.50992 7.89605i −0.355197 0.329575i
\(575\) 8.33712 + 4.01495i 0.347682 + 0.167435i
\(576\) 2.07911 1.41751i 0.0866295 0.0590630i
\(577\) −13.5321 34.4792i −0.563348 1.43539i −0.874499 0.485027i \(-0.838810\pi\)
0.311151 0.950361i \(-0.399286\pi\)
\(578\) 0.658213 0.203032i 0.0273780 0.00844501i
\(579\) 22.7798 21.1366i 0.946698 0.878408i
\(580\) 1.60494 2.01253i 0.0666416 0.0835659i
\(581\) −36.2085 + 45.4041i −1.50218 + 1.88368i
\(582\) 6.00698 5.57367i 0.248998 0.231036i
\(583\) −57.6247 + 17.7749i −2.38657 + 0.736159i
\(584\) 12.4443 + 31.7076i 0.514949 + 1.31207i
\(585\) −8.93141 + 6.08933i −0.369268 + 0.251763i
\(586\) −0.917872 0.442024i −0.0379169 0.0182598i
\(587\) −13.3626 12.3987i −0.551533 0.511747i 0.354443 0.935078i \(-0.384671\pi\)
−0.905975 + 0.423330i \(0.860861\pi\)
\(588\) 17.5230 2.64117i 0.722638 0.108920i
\(589\) −1.18949 + 15.8726i −0.0490121 + 0.654021i
\(590\) −7.25800 + 18.4931i −0.298807 + 0.761348i
\(591\) −4.02274 17.6248i −0.165474 0.724987i
\(592\) 0.0703167 + 0.938311i 0.00289000 + 0.0385644i
\(593\) −12.0055 3.70320i −0.493006 0.152072i 0.0382761 0.999267i \(-0.487813\pi\)
−0.531282 + 0.847195i \(0.678290\pi\)
\(594\) 5.66637 2.72878i 0.232494 0.111963i
\(595\) −6.15544 + 10.6615i −0.252348 + 0.437080i
\(596\) −7.70561 13.3465i −0.315634 0.546694i
\(597\) −11.4404 7.79995i −0.468225 0.319231i
\(598\) −0.288517 + 1.26408i −0.0117983 + 0.0516919i
\(599\) 22.7007 + 3.42158i 0.927525 + 0.139802i 0.595396 0.803432i \(-0.296995\pi\)
0.332129 + 0.943234i \(0.392233\pi\)
\(600\) −25.2547 31.6684i −1.03102 1.29286i
\(601\) 12.9797 0.529453 0.264727 0.964324i \(-0.414718\pi\)
0.264727 + 0.964324i \(0.414718\pi\)
\(602\) 2.44687 15.5741i 0.0997271 0.634754i
\(603\) 32.4557 1.32170
\(604\) 14.4989 + 18.1810i 0.589950 + 0.739774i
\(605\) −22.4716 3.38704i −0.913599 0.137703i
\(606\) −2.71378 + 11.8899i −0.110240 + 0.482993i
\(607\) −19.5176 13.3069i −0.792196 0.540110i 0.0982702 0.995160i \(-0.468669\pi\)
−0.890466 + 0.455050i \(0.849621\pi\)
\(608\) 10.6051 + 18.3685i 0.430092 + 0.744941i
\(609\) −1.87141 + 3.24138i −0.0758334 + 0.131347i
\(610\) −24.4519 + 11.7754i −0.990029 + 0.476773i
\(611\) 0.444847 + 0.137217i 0.0179966 + 0.00555122i
\(612\) 0.230825 + 3.08015i 0.00933056 + 0.124508i
\(613\) −4.42322 19.3794i −0.178652 0.782727i −0.982253 0.187559i \(-0.939943\pi\)
0.803601 0.595168i \(-0.202915\pi\)
\(614\) −0.307294 + 0.782973i −0.0124014 + 0.0315982i
\(615\) −2.85302 + 38.0709i −0.115045 + 1.53517i
\(616\) −35.0043 + 5.27605i −1.41036 + 0.212578i
\(617\) −30.7312 28.5144i −1.23719 1.14794i −0.983548 0.180646i \(-0.942181\pi\)
−0.253642 0.967298i \(-0.581628\pi\)
\(618\) 6.37736 + 3.07118i 0.256535 + 0.123541i
\(619\) −5.48028 + 3.73639i −0.220271 + 0.150178i −0.668429 0.743776i \(-0.733033\pi\)
0.448157 + 0.893955i \(0.352080\pi\)
\(620\) −8.56581 21.8253i −0.344011 0.876526i
\(621\) 2.59791 0.801348i 0.104250 0.0321570i
\(622\) −3.14862 + 2.92149i −0.126248 + 0.117141i
\(623\) 23.9934 30.0867i 0.961274 1.20540i
\(624\) −2.91580 + 3.65630i −0.116725 + 0.146369i
\(625\) 5.01175 4.65023i 0.200470 0.186009i
\(626\) −15.4497 + 4.76561i −0.617496 + 0.190472i
\(627\) −12.4942 31.8347i −0.498971 1.27136i
\(628\) 6.72747 4.58671i 0.268455 0.183030i
\(629\) 0.615066 + 0.296200i 0.0245243 + 0.0118103i
\(630\) 12.5861 + 11.6782i 0.501443 + 0.465271i
\(631\) −28.6091 + 4.31213i −1.13891 + 0.171663i −0.691302 0.722566i \(-0.742963\pi\)
−0.447609 + 0.894229i \(0.647724\pi\)
\(632\) −2.37896 + 31.7450i −0.0946300 + 1.26275i
\(633\) −7.30519 + 18.6133i −0.290355 + 0.739813i
\(634\) 2.56512 + 11.2385i 0.101874 + 0.446339i
\(635\) 1.19632 + 15.9637i 0.0474744 + 0.633502i
\(636\) 47.1820 + 14.5537i 1.87089 + 0.577093i
\(637\) 7.06709 3.40333i 0.280008 0.134845i
\(638\) 0.688119 1.19186i 0.0272429 0.0471860i
\(639\) 8.22774 + 14.2509i 0.325484 + 0.563755i
\(640\) −31.3476 21.3724i −1.23912 0.844819i
\(641\) 0.718095 3.14618i 0.0283631 0.124267i −0.958764 0.284202i \(-0.908271\pi\)
0.987128 + 0.159935i \(0.0511285\pi\)
\(642\) 15.0127 + 2.26279i 0.592502 + 0.0893054i
\(643\) −13.2795 16.6520i −0.523694 0.656691i 0.447695 0.894186i \(-0.352245\pi\)
−0.971389 + 0.237495i \(0.923674\pi\)
\(644\) −6.62156 −0.260926
\(645\) −45.0610 + 25.6425i −1.77428 + 1.00967i
\(646\) 2.51621 0.0989989
\(647\) −7.96585 9.98885i −0.313170 0.392702i 0.600189 0.799858i \(-0.295092\pi\)
−0.913359 + 0.407156i \(0.866521\pi\)
\(648\) −26.3536 3.97217i −1.03527 0.156042i
\(649\) 7.59923 33.2944i 0.298296 1.30692i
\(650\) −6.41001 4.37027i −0.251421 0.171416i
\(651\) 17.0455 + 29.5236i 0.668064 + 1.15712i
\(652\) −5.62399 + 9.74104i −0.220253 + 0.381489i
\(653\) −18.4367 + 8.87865i −0.721484 + 0.347449i −0.758329 0.651872i \(-0.773984\pi\)
0.0368443 + 0.999321i \(0.488269\pi\)
\(654\) −14.0653 4.33856i −0.549996 0.169651i
\(655\) 3.32021 + 44.3051i 0.129731 + 1.73114i
\(656\) 1.48098 + 6.48858i 0.0578224 + 0.253337i
\(657\) −10.3755 + 26.4364i −0.404788 + 1.03138i
\(658\) 0.0552568 0.737351i 0.00215413 0.0287449i
\(659\) −13.4859 + 2.03267i −0.525334 + 0.0791814i −0.406355 0.913715i \(-0.633200\pi\)
−0.118979 + 0.992897i \(0.537962\pi\)
\(660\) 36.9275 + 34.2637i 1.43740 + 1.33371i
\(661\) 11.1901 + 5.38886i 0.435244 + 0.209603i 0.638659 0.769490i \(-0.279490\pi\)
−0.203414 + 0.979093i \(0.565204\pi\)
\(662\) 2.90407 1.97996i 0.112870 0.0769533i
\(663\) 1.23958 + 3.15841i 0.0481415 + 0.122662i
\(664\) −38.6110 + 11.9099i −1.49840 + 0.462194i
\(665\) −32.9661 + 30.5881i −1.27837 + 1.18616i
\(666\) 0.593622 0.744378i 0.0230024 0.0288441i
\(667\) 0.370926 0.465126i 0.0143623 0.0180098i
\(668\) −15.2839 + 14.1814i −0.591352 + 0.548695i
\(669\) −2.66272 + 0.821340i −0.102947 + 0.0317548i
\(670\) 14.2283 + 36.2531i 0.549687 + 1.40058i
\(671\) 38.5469 26.2808i 1.48808 1.01456i
\(672\) 40.9286 + 19.7102i 1.57885 + 0.760336i
\(673\) 14.0095 + 12.9989i 0.540027 + 0.501072i 0.902364 0.430975i \(-0.141830\pi\)
−0.362337 + 0.932047i \(0.618021\pi\)
\(674\) −9.34505 + 1.40854i −0.359958 + 0.0542549i
\(675\) −1.21565 + 16.2217i −0.0467903 + 0.624374i
\(676\) 5.96850 15.2075i 0.229558 0.584904i
\(677\) −6.60821 28.9524i −0.253974 1.11273i −0.927575 0.373637i \(-0.878110\pi\)
0.673601 0.739095i \(-0.264747\pi\)
\(678\) 0.390918 + 5.21644i 0.0150131 + 0.200336i
\(679\) 17.7006 + 5.45992i 0.679288 + 0.209533i
\(680\) −7.71728 + 3.71645i −0.295944 + 0.142519i
\(681\) 11.4204 19.7808i 0.437632 0.758001i
\(682\) −6.26763 10.8558i −0.240000 0.415692i
\(683\) −12.6905 8.65223i −0.485588 0.331068i 0.295655 0.955295i \(-0.404462\pi\)
−0.781244 + 0.624226i \(0.785414\pi\)
\(684\) −2.51075 + 11.0003i −0.0960009 + 0.420607i
\(685\) 26.6897 + 4.02283i 1.01976 + 0.153704i
\(686\) 2.72492 + 3.41694i 0.104038 + 0.130459i
\(687\) 17.6381 0.672935
\(688\) −6.18879 + 6.58704i −0.235946 + 0.251129i
\(689\) 21.8553 0.832620
\(690\) −4.22272 5.29512i −0.160756 0.201582i
\(691\) 39.3167 + 5.92604i 1.49568 + 0.225437i 0.845348 0.534215i \(-0.179393\pi\)
0.650329 + 0.759652i \(0.274631\pi\)
\(692\) 1.42174 6.22907i 0.0540466 0.236794i
\(693\) −24.3862 16.6262i −0.926354 0.631577i
\(694\) 12.3398 + 21.3732i 0.468413 + 0.811316i
\(695\) 5.09099 8.81785i 0.193112 0.334480i
\(696\) −2.34625 + 1.12989i −0.0889344 + 0.0428285i
\(697\) 4.61413 + 1.42327i 0.174773 + 0.0539102i
\(698\) 0.959892 + 12.8089i 0.0363324 + 0.484823i
\(699\) −6.75766 29.6073i −0.255598 1.11985i
\(700\) 14.4748 36.8811i 0.547095 1.39398i
\(701\) −0.905970 + 12.0893i −0.0342180 + 0.456608i 0.953609 + 0.301049i \(0.0973368\pi\)
−0.987827 + 0.155559i \(0.950282\pi\)
\(702\) −2.25387 + 0.339716i −0.0850669 + 0.0128218i
\(703\) 1.82806 + 1.69619i 0.0689467 + 0.0639732i
\(704\) −4.67654 2.25210i −0.176254 0.0848794i
\(705\) −2.00916 + 1.36982i −0.0756694 + 0.0515905i
\(706\) −5.10067 12.9963i −0.191966 0.489122i
\(707\) −26.3434 + 8.12585i −0.990744 + 0.305604i
\(708\) −20.4975 + 19.0189i −0.770345 + 0.714776i
\(709\) −20.1014 + 25.2064i −0.754924 + 0.946645i −0.999737 0.0229253i \(-0.992702\pi\)
0.244813 + 0.969570i \(0.421273\pi\)
\(710\) −12.3113 + 15.4379i −0.462034 + 0.579372i
\(711\) −19.4565 + 18.0530i −0.729677 + 0.677041i
\(712\) 25.5853 7.89203i 0.958851 0.295766i
\(713\) −1.97969 5.04416i −0.0741398 0.188905i
\(714\) 4.45273 3.03582i 0.166639 0.113613i
\(715\) 20.0895 + 9.67457i 0.751303 + 0.361808i
\(716\) −4.60012 4.26829i −0.171914 0.159513i
\(717\) 5.03444 0.758820i 0.188015 0.0283386i
\(718\) −1.88732 + 25.1845i −0.0704342 + 0.939879i
\(719\) 1.53986 3.92351i 0.0574272 0.146322i −0.899281 0.437372i \(-0.855909\pi\)
0.956708 + 0.291050i \(0.0940046\pi\)
\(720\) −2.19036 9.59659i −0.0816298 0.357644i
\(721\) 1.19572 + 15.9558i 0.0445310 + 0.594225i
\(722\) −3.72280 1.14833i −0.138548 0.0427364i
\(723\) −5.97226 + 2.87609i −0.222111 + 0.106963i
\(724\) 20.1648 34.9264i 0.749417 1.29803i
\(725\) 1.77984 + 3.08277i 0.0661015 + 0.114491i
\(726\) 8.21956 + 5.60400i 0.305056 + 0.207984i
\(727\) 2.63200 11.5315i 0.0976155 0.427681i −0.902379 0.430943i \(-0.858181\pi\)
0.999995 + 0.00326159i \(0.00103820\pi\)
\(728\) 12.6862 + 1.91214i 0.470183 + 0.0708687i
\(729\) −4.68816 5.87876i −0.173635 0.217732i
\(730\) −34.0781 −1.26129
\(731\) 1.89371 + 6.27804i 0.0700415 + 0.232202i
\(732\) −38.1990 −1.41187
\(733\) −1.05776 1.32639i −0.0390692 0.0489913i 0.761913 0.647679i \(-0.224260\pi\)
−0.800982 + 0.598688i \(0.795689\pi\)
\(734\) −14.4414 2.17669i −0.533041 0.0803430i
\(735\) −9.11724 + 39.9452i −0.336294 + 1.47340i
\(736\) −5.96597 4.06753i −0.219909 0.149931i
\(737\) −33.4738 57.9783i −1.23302 2.13566i
\(738\) 3.36717 5.83211i 0.123947 0.214683i
\(739\) −34.8416 + 16.7788i −1.28167 + 0.617219i −0.945818 0.324697i \(-0.894738\pi\)
−0.335850 + 0.941916i \(0.609023\pi\)
\(740\) −3.51014 1.08274i −0.129035 0.0398022i
\(741\) 0.926227 + 12.3596i 0.0340258 + 0.454043i
\(742\) −7.72449 33.8432i −0.283575 1.24242i
\(743\) 9.19081 23.4178i 0.337178 0.859116i −0.657247 0.753675i \(-0.728279\pi\)
0.994426 0.105441i \(-0.0336254\pi\)
\(744\) −1.77256 + 23.6531i −0.0649851 + 0.867165i
\(745\) 35.2342 5.31070i 1.29088 0.194569i
\(746\) 3.13164 + 2.90574i 0.114657 + 0.106387i
\(747\) −30.3526 14.6170i −1.11054 0.534810i
\(748\) 5.26426 3.58911i 0.192480 0.131231i
\(749\) 12.5383 + 31.9470i 0.458138 + 1.16732i
\(750\) 12.7032 3.91840i 0.463854 0.143080i
\(751\) −25.8767 + 24.0100i −0.944253 + 0.876139i −0.992444 0.122699i \(-0.960845\pi\)
0.0481906 + 0.998838i \(0.484655\pi\)
\(752\) −0.264306 + 0.331429i −0.00963823 + 0.0120860i
\(753\) 36.7548 46.0890i 1.33942 1.67958i
\(754\) −0.365628 + 0.339253i −0.0133154 + 0.0123549i
\(755\) −51.3775 + 15.8479i −1.86982 + 0.576763i
\(756\) −4.25271 10.8357i −0.154669 0.394091i
\(757\) −20.5724 + 14.0260i −0.747716 + 0.509784i −0.876212 0.481926i \(-0.839937\pi\)
0.128496 + 0.991710i \(0.458985\pi\)
\(758\) 15.5393 + 7.48331i 0.564411 + 0.271806i
\(759\) 8.53449 + 7.91885i 0.309782 + 0.287436i
\(760\) −30.9400 + 4.66346i −1.12231 + 0.169161i
\(761\) 3.47115 46.3193i 0.125829 1.67907i −0.475225 0.879864i \(-0.657633\pi\)
0.601055 0.799208i \(-0.294747\pi\)
\(762\) 2.56024 6.52339i 0.0927477 0.236317i
\(763\) −7.40387 32.4385i −0.268038 1.17435i
\(764\) 2.07922 + 27.7452i 0.0752234 + 1.00379i
\(765\) −6.82428 2.10501i −0.246732 0.0761069i
\(766\) 15.0700 7.25732i 0.544501 0.262218i
\(767\) −6.18843 + 10.7187i −0.223451 + 0.387029i
\(768\) 11.0901 + 19.2086i 0.400180 + 0.693132i
\(769\) 36.4025 + 24.8188i 1.31271 + 0.894989i 0.998521 0.0543714i \(-0.0173155\pi\)
0.314188 + 0.949361i \(0.398268\pi\)
\(770\) 7.88083 34.5282i 0.284005 1.24431i
\(771\) −5.10111 0.768869i −0.183712 0.0276901i
\(772\) 13.1859 + 16.5347i 0.474573 + 0.595095i
\(773\) −33.9136 −1.21979 −0.609893 0.792484i \(-0.708788\pi\)
−0.609893 + 0.792484i \(0.708788\pi\)
\(774\) 9.12392 0.626534i 0.327952 0.0225203i
\(775\) 32.4228 1.16466
\(776\) 8.03563 + 10.0764i 0.288462 + 0.361720i
\(777\) 5.28144 + 0.796048i 0.189470 + 0.0285581i
\(778\) −3.80253 + 16.6600i −0.136327 + 0.597289i
\(779\) 14.5739 + 9.93633i 0.522165 + 0.356006i
\(780\) −9.12844 15.8109i −0.326851 0.566122i
\(781\) 16.9717 29.3958i 0.607294 1.05186i
\(782\) −0.771772 + 0.371666i −0.0275985 + 0.0132907i
\(783\) 0.999374 + 0.308266i 0.0357147 + 0.0110165i
\(784\) 0.533772 + 7.12269i 0.0190633 + 0.254382i
\(785\) 4.18912 + 18.3537i 0.149516 + 0.655072i
\(786\) 7.10559 18.1047i 0.253448 0.645775i
\(787\) −0.161937 + 2.16090i −0.00577243 + 0.0770277i −0.999346 0.0361605i \(-0.988487\pi\)
0.993574 + 0.113188i \(0.0361063\pi\)
\(788\) 12.1658 1.83369i 0.433387 0.0653226i
\(789\) −16.2048 15.0358i −0.576905 0.535289i
\(790\) −28.6948 13.8187i −1.02092 0.491647i
\(791\) −9.77010 + 6.66114i −0.347385 + 0.236843i
\(792\) −7.50243 19.1159i −0.266587 0.679253i
\(793\) −16.1569 + 4.98375i −0.573749 + 0.176978i
\(794\) 6.41668 5.95381i 0.227719 0.211293i
\(795\) −71.1783 + 89.2547i −2.52443 + 3.16554i
\(796\) 5.87532 7.36742i 0.208245 0.261131i
\(797\) −1.22757 + 1.13902i −0.0434827 + 0.0403461i −0.701615 0.712556i \(-0.747537\pi\)
0.658132 + 0.752902i \(0.271347\pi\)
\(798\) 18.8117 5.80265i 0.665928 0.205412i
\(799\) 0.112363 + 0.286297i 0.00397513 + 0.0101285i
\(800\) 35.6972 24.3379i 1.26209 0.860475i
\(801\) 20.1130 + 9.68589i 0.710657 + 0.342234i
\(802\) −15.3193 14.2142i −0.540943 0.501922i
\(803\) 57.9265 8.73101i 2.04418 0.308111i
\(804\) −4.09636 + 54.6622i −0.144468 + 1.92779i
\(805\) 5.59325 14.2514i 0.197136 0.502295i
\(806\) 1.01092 + 4.42912i 0.0356080 + 0.156009i
\(807\) −3.09886 41.3514i −0.109085 1.45564i
\(808\) −18.3289 5.65372i −0.644809 0.198897i
\(809\) −40.1149 + 19.3183i −1.41036 + 0.679195i −0.975235 0.221173i \(-0.929011\pi\)
−0.435129 + 0.900368i \(0.643297\pi\)
\(810\) 13.3319 23.0915i 0.468434 0.811351i
\(811\) −11.4175 19.7757i −0.400923 0.694420i 0.592914 0.805266i \(-0.297977\pi\)
−0.993838 + 0.110846i \(0.964644\pi\)
\(812\) −2.10460 1.43489i −0.0738571 0.0503549i
\(813\) 1.04510 4.57889i 0.0366533 0.160589i
\(814\) −1.94199 0.292707i −0.0680666 0.0102594i
\(815\) −16.2147 20.3326i −0.567977 0.712220i
\(816\) −3.08964 −0.108159
\(817\) −0.149424 + 23.9536i −0.00522769 + 0.838029i
\(818\) −1.08339 −0.0378800
\(819\) 6.66928 + 8.36301i 0.233043 + 0.292227i
\(820\) −25.6920 3.87244i −0.897202 0.135231i
\(821\) −2.93904 + 12.8768i −0.102573 + 0.449403i 0.897393 + 0.441231i \(0.145458\pi\)
−0.999967 + 0.00817131i \(0.997399\pi\)
\(822\) −9.76246 6.65593i −0.340505 0.232152i
\(823\) 19.3881 + 33.5812i 0.675826 + 1.17057i 0.976227 + 0.216753i \(0.0695465\pi\)
−0.300400 + 0.953813i \(0.597120\pi\)
\(824\) −5.56634 + 9.64119i −0.193913 + 0.335867i
\(825\) −62.7632 + 30.2252i −2.18514 + 1.05231i
\(826\) 18.7853 + 5.79448i 0.653623 + 0.201616i
\(827\) 3.95600 + 52.7891i 0.137564 + 1.83566i 0.458661 + 0.888611i \(0.348329\pi\)
−0.321097 + 0.947046i \(0.604052\pi\)
\(828\) −0.854744 3.74488i −0.0297044 0.130143i
\(829\) 16.6800 42.5000i 0.579321 1.47609i −0.277630 0.960688i \(-0.589549\pi\)
0.856951 0.515398i \(-0.172356\pi\)
\(830\) 3.02096 40.3119i 0.104859 1.39925i
\(831\) 70.8513 10.6791i 2.45780 0.370454i
\(832\) 1.37899 + 1.27952i 0.0478079 + 0.0443593i
\(833\) 4.66895 + 2.24845i 0.161769 + 0.0779041i
\(834\) −3.68272 + 2.51084i −0.127522 + 0.0869432i
\(835\) −17.6118 44.8741i −0.609481 1.55293i
\(836\) 22.2403 6.86021i 0.769196 0.237265i
\(837\) 6.98295 6.47923i 0.241366 0.223955i
\(838\) 16.6291 20.8522i 0.574443 0.720329i
\(839\) −15.8922 + 19.9282i −0.548661 + 0.687999i −0.976417 0.215895i \(-0.930733\pi\)
0.427755 + 0.903895i \(0.359304\pi\)
\(840\) −49.1255 + 45.5818i −1.69499 + 1.57272i
\(841\) −27.4929 + 8.48044i −0.948032 + 0.292429i
\(842\) −1.28023 3.26198i −0.0441197 0.112415i
\(843\) 8.12763 5.54132i 0.279930 0.190853i
\(844\) −12.2605 5.90435i −0.422024 0.203236i
\(845\) 27.6890 + 25.6916i 0.952530 + 0.883819i
\(846\) 0.424147 0.0639299i 0.0145825 0.00219795i
\(847\) −1.68051 + 22.4249i −0.0577431 + 0.770528i
\(848\) −7.27083 + 18.5258i −0.249681 + 0.636178i
\(849\) 14.9766 + 65.6167i 0.513995 + 2.25196i
\(850\) −0.383025 5.11112i −0.0131377 0.175310i
\(851\) −0.811246 0.250236i −0.0278092 0.00857799i
\(852\) −25.0399 + 12.0586i −0.857852 + 0.413120i
\(853\) 11.6848 20.2387i 0.400081 0.692960i −0.593654 0.804720i \(-0.702315\pi\)
0.993735 + 0.111760i \(0.0356487\pi\)
\(854\) 13.4279 + 23.2578i 0.459493 + 0.795865i
\(855\) −21.5548 14.6958i −0.737157 0.502585i
\(856\) −5.31343 + 23.2797i −0.181609 + 0.795683i
\(857\) 45.9157 + 6.92067i 1.56845 + 0.236406i 0.875008 0.484108i \(-0.160856\pi\)
0.693441 + 0.720514i \(0.256094\pi\)
\(858\) −6.08582 7.63138i −0.207767 0.260531i
\(859\) −6.94037 −0.236802 −0.118401 0.992966i \(-0.537777\pi\)
−0.118401 + 0.992966i \(0.537777\pi\)
\(860\) −15.1107 31.8851i −0.515272 1.08727i
\(861\) 37.7785 1.28749
\(862\) 0.624212 + 0.782737i 0.0212607 + 0.0266601i
\(863\) −27.6823 4.17244i −0.942317 0.142031i −0.340123 0.940381i \(-0.610469\pi\)
−0.602194 + 0.798350i \(0.705707\pi\)
\(864\) 2.82457 12.3753i 0.0960939 0.421015i
\(865\) 12.2057 + 8.32168i 0.415005 + 0.282945i
\(866\) 7.59930 + 13.1624i 0.258235 + 0.447275i
\(867\) −1.12079 + 1.94127i −0.0380642 + 0.0659291i
\(868\) −20.9033 + 10.0665i −0.709504 + 0.341679i
\(869\) 52.3164 + 16.1375i 1.77471 + 0.547426i
\(870\) −0.194698 2.59807i −0.00660089 0.0880828i
\(871\) 5.39905 + 23.6548i 0.182940 + 0.801511i
\(872\) 8.45769 21.5498i 0.286414 0.729770i
\(873\) −0.803017 + 10.7155i −0.0271780 + 0.362665i
\(874\) −3.09418 + 0.466373i −0.104662 + 0.0157753i
\(875\) 22.0285 + 20.4395i 0.744701 + 0.690981i
\(876\) −43.2149 20.8112i −1.46009 0.703145i
\(877\) 34.7495 23.6918i 1.17341 0.800017i 0.190065 0.981772i \(-0.439130\pi\)
0.983344 + 0.181755i \(0.0581777\pi\)
\(878\) 9.58506 + 24.4223i 0.323480 + 0.824214i
\(879\) 3.16803 0.977209i 0.106855 0.0329604i
\(880\) −14.8841 + 13.8104i −0.501743 + 0.465549i
\(881\) −10.5507 + 13.2302i −0.355463 + 0.445737i −0.927125 0.374753i \(-0.877728\pi\)
0.571662 + 0.820490i \(0.306299\pi\)
\(882\) 4.50617 5.65055i 0.151731 0.190264i
\(883\) −12.0358 + 11.1676i −0.405037 + 0.375819i −0.856219 0.516613i \(-0.827193\pi\)
0.451183 + 0.892432i \(0.351002\pi\)
\(884\) −2.20652 + 0.680620i −0.0742132 + 0.0228917i
\(885\) −23.6195 60.1815i −0.793961 2.02298i
\(886\) 8.24402 5.62068i 0.276963 0.188830i
\(887\) 22.4935 + 10.8323i 0.755258 + 0.363713i 0.771562 0.636154i \(-0.219476\pi\)
−0.0163040 + 0.999867i \(0.505190\pi\)
\(888\) 2.72415 + 2.52764i 0.0914163 + 0.0848220i
\(889\) 15.6642 2.36099i 0.525360 0.0791852i
\(890\) −2.00182 + 26.7124i −0.0671012 + 0.895403i
\(891\) −16.7456 + 42.6670i −0.560997 + 1.42940i
\(892\) −0.421986 1.84884i −0.0141291 0.0619038i
\(893\) 0.0839587 + 1.12035i 0.00280957 + 0.0374911i
\(894\) −14.9052 4.59764i −0.498504 0.153768i
\(895\) 13.0722 6.29525i 0.436956 0.210427i
\(896\) −18.7717 + 32.5135i −0.627118 + 1.08620i
\(897\) −2.10972 3.65414i −0.0704414 0.122008i
\(898\) 2.10965 + 1.43834i 0.0704000 + 0.0479979i
\(899\) 0.463845 2.03224i 0.0154701 0.0677789i
\(900\) 22.7269 + 3.42552i 0.757562 + 0.114184i
\(901\) 9.00252 + 11.2888i 0.299917 + 0.376085i
\(902\) −13.8912 −0.462525
\(903\) 28.6357 + 42.5689i 0.952935 + 1.41660i
\(904\) −8.22733 −0.273637
\(905\) 58.1377 + 72.9023i 1.93256 + 2.42335i
\(906\) 23.2736 + 3.50793i 0.773213 + 0.116543i
\(907\) 10.9857 48.1316i 0.364775 1.59818i −0.376126 0.926568i \(-0.622744\pi\)
0.740901 0.671614i \(-0.234399\pi\)
\(908\) 12.8435 + 8.75656i 0.426227 + 0.290597i
\(909\) −7.99617 13.8498i −0.265216 0.459368i
\(910\) −6.41775 + 11.1159i −0.212746 + 0.368487i
\(911\) 18.3695 8.84627i 0.608608 0.293090i −0.104083 0.994569i \(-0.533191\pi\)
0.712690 + 0.701479i \(0.247476\pi\)
\(912\) −10.7849 3.32670i −0.357123 0.110158i
\(913\) 5.19308 + 69.2969i 0.171866 + 2.29339i
\(914\) 0.370059 + 1.62134i 0.0122405 + 0.0536290i
\(915\) 32.2667 82.2143i 1.06671 2.71792i
\(916\) −0.897042 + 11.9702i −0.0296391 + 0.395506i
\(917\) 43.4737 6.55261i 1.43563 0.216386i
\(918\) −1.10388 1.02425i −0.0364333 0.0338052i
\(919\) −5.57335 2.68398i −0.183848 0.0885364i 0.339696 0.940535i \(-0.389676\pi\)
−0.523543 + 0.851999i \(0.675390\pi\)
\(920\) 8.80110 6.00049i 0.290164 0.197830i
\(921\) −1.00002 2.54801i −0.0329517 0.0839596i
\(922\) −17.6016 + 5.42937i −0.579677 + 0.178807i
\(923\) −9.01780 + 8.36729i −0.296824 + 0.275413i
\(924\) 31.0799 38.9729i 1.02245 1.28211i
\(925\) 3.16717 3.97150i 0.104136 0.130582i
\(926\) 9.60301 8.91029i 0.315575 0.292810i
\(927\) −8.86957 + 2.73590i −0.291315 + 0.0898588i
\(928\) −1.01479 2.58565i −0.0333123 0.0848783i
\(929\) 21.1067 14.3903i 0.692488 0.472131i −0.165227 0.986256i \(-0.552836\pi\)
0.857715 + 0.514125i \(0.171883\pi\)
\(930\) −21.3804 10.2963i −0.701092 0.337628i
\(931\) 13.8768 + 12.8758i 0.454793 + 0.421986i
\(932\) 20.4368 3.08036i 0.669431 0.100900i
\(933\) 1.04456 13.9387i 0.0341975 0.456334i
\(934\) 9.71715 24.7589i 0.317955 0.810136i
\(935\) 3.27799 + 14.3618i 0.107202 + 0.469682i
\(936\) 0.556174 + 7.42162i 0.0181791 + 0.242583i
\(937\) 16.3624 + 5.04714i 0.534537 + 0.164883i 0.550260 0.834994i \(-0.314529\pi\)
−0.0157229 + 0.999876i \(0.505005\pi\)
\(938\) 34.7215 16.7210i 1.13370 0.545960i
\(939\) 26.3076 45.5661i 0.858515 1.48699i
\(940\) −0.827456 1.43320i −0.0269886 0.0467457i
\(941\) 0.0276737 + 0.0188676i 0.000902138 + 0.000615067i 0.563771 0.825931i \(-0.309350\pi\)
−0.562869 + 0.826546i \(0.690302\pi\)
\(942\) 1.83381 8.03444i 0.0597487 0.261776i
\(943\) −5.93779 0.894978i −0.193361 0.0291445i
\(944\) −7.02699 8.81157i −0.228709 0.286792i
\(945\) 26.9136 0.875500
\(946\) −10.5293 15.6526i −0.342339 0.508910i
\(947\) −26.8630 −0.872929 −0.436465 0.899721i \(-0.643770\pi\)
−0.436465 + 0.899721i \(0.643770\pi\)
\(948\) −27.9494 35.0474i −0.907753 1.13829i
\(949\) −20.9937 3.16429i −0.681484 0.102717i
\(950\) 4.16627 18.2536i 0.135172 0.592225i
\(951\) −30.9953 21.1323i −1.00509 0.685261i
\(952\) 4.23798 + 7.34040i 0.137354 + 0.237904i
\(953\) 17.5119 30.3315i 0.567267 0.982535i −0.429568 0.903034i \(-0.641334\pi\)
0.996835 0.0795003i \(-0.0253325\pi\)
\(954\) 18.1432 8.73729i 0.587407 0.282880i
\(955\) −61.4714 18.9614i −1.98917 0.613577i
\(956\) 0.258935 + 3.45525i 0.00837455 + 0.111751i
\(957\) 0.996593 + 4.36636i 0.0322153 + 0.141144i
\(958\) 1.60171 4.08109i 0.0517489 0.131854i
\(959\) 1.99596 26.6343i 0.0644530 0.860065i
\(960\) −9.71652 + 1.46453i −0.313599 + 0.0472675i
\(961\) 8.80662 + 8.17135i 0.284085 + 0.263592i
\(962\) 0.641277 + 0.308823i 0.0206756 + 0.00995684i
\(963\) −16.4493 + 11.2150i −0.530073 + 0.361398i
\(964\) −1.64814 4.19938i −0.0530829 0.135253i
\(965\) −46.7252 + 14.4128i −1.50414 + 0.463965i
\(966\) −4.91283 + 4.55844i −0.158068 + 0.146666i
\(967\) 11.8980 14.9197i 0.382615 0.479784i −0.552811 0.833307i \(-0.686445\pi\)
0.935426 + 0.353523i \(0.115016\pi\)
\(968\) −9.75531 + 12.2328i −0.313547 + 0.393176i
\(969\) −6.00254 + 5.56955i −0.192829 + 0.178920i
\(970\) −12.3213 + 3.80062i −0.395613 + 0.122030i
\(971\) −3.88871 9.90828i −0.124795 0.317972i 0.854799 0.518959i \(-0.173680\pi\)
−0.979594 + 0.200987i \(0.935585\pi\)
\(972\) 22.7414 15.5048i 0.729430 0.497317i
\(973\) −9.07772 4.37160i −0.291018 0.140147i
\(974\) −1.65775 1.53817i −0.0531178 0.0492861i
\(975\) 24.9649 3.76285i 0.799515 0.120508i
\(976\) 1.15059 15.3535i 0.0368294 0.491455i
\(977\) 20.8191 53.0462i 0.666062 1.69710i −0.0497095 0.998764i \(-0.515830\pi\)
0.715772 0.698335i \(-0.246075\pi\)
\(978\) 2.53327 + 11.0990i 0.0810052 + 0.354907i
\(979\) −3.44117 45.9192i −0.109980 1.46758i
\(980\) −26.6454 8.21901i −0.851156 0.262547i
\(981\) 17.3901 8.37463i 0.555223 0.267381i
\(982\) 3.04725 5.27799i 0.0972417 0.168428i
\(983\) −15.0875 26.1323i −0.481216 0.833491i 0.518551 0.855047i \(-0.326472\pi\)
−0.999768 + 0.0215553i \(0.993138\pi\)
\(984\) 21.7178 + 14.8069i 0.692337 + 0.472028i
\(985\) −6.32985 + 27.7329i −0.201686 + 0.883643i
\(986\) −0.325841 0.0491126i −0.0103769 0.00156406i
\(987\) 1.50028 + 1.88130i 0.0477545 + 0.0598823i
\(988\) −8.43505 −0.268355
\(989\) −3.49232 7.36911i −0.111049 0.234324i
\(990\) 20.5450 0.652962
\(991\) −11.8444 14.8524i −0.376249 0.471802i 0.557269 0.830332i \(-0.311849\pi\)
−0.933518 + 0.358531i \(0.883278\pi\)
\(992\) −25.0174 3.77076i −0.794302 0.119722i
\(993\) −2.54522 + 11.1513i −0.0807701 + 0.353877i
\(994\) 16.1441 + 11.0069i 0.512060 + 0.349117i
\(995\) 10.8937 + 18.8685i 0.345355 + 0.598172i
\(996\) 28.4491 49.2752i 0.901443 1.56135i
\(997\) 17.8704 8.60594i 0.565962 0.272553i −0.128946 0.991652i \(-0.541159\pi\)
0.694908 + 0.719099i \(0.255445\pi\)
\(998\) 18.2445 + 5.62767i 0.577518 + 0.178141i
\(999\) −0.111530 1.48826i −0.00352864 0.0470865i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 731.2.u.b.52.18 348
43.24 even 21 inner 731.2.u.b.239.18 yes 348
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.u.b.52.18 348 1.1 even 1 trivial
731.2.u.b.239.18 yes 348 43.24 even 21 inner